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THE AVERAGE DENSITY OF SELF-CONFORMAL MEASURES

Published online by Cambridge University Press:  05 July 2001

M. ZÄHLE
M. ZÄHLE
Affiliation:
University of Jena, Germany; [email protected]
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Abstract

The paper calculates the average density of the normalized Hausdorff measure on the fractal set generated by a conformal iterated function system. It equals almost everywhere a positive constant given by a truncated generalized s-energy integral, where s is the corresponding Hausdorff dimension. As a main tool a conditional Gibbs measure is determined. The appendix proves an appropriate extension of Birkhoff's ergodic theorem which is also of independent interest.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 63 , Issue 3 , June 2001 , pp. 721 - 734
Copyright
The London Mathematical Society 2001

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